Question

Two square sheets of cardboard used for making book covers differ in area by 64 square inches. An edge of the larger square is 2 inches greater than an edge of the smaller square. Find the length of an edge of the smaller square.

Answer 1

Answer:

15 inches

Step-by-step explanation:

We assume that the edge of the small square is x (inches).

As the edge of the larger square is 2 inches greater than that of the smaller one, so that the edge of the larger square = edge of the small square  + 2 = x + 2 (inches)

The equation to calculate the are of a square is: Area = Edge^2

So that:

+) The area of the larger square is: Area large square = $(x+2)^{2}$ (square inches)

+) The area of the smaller square is: Area small square = $x^{2}$(square inches)

As difference in area of both squares are 64 square inches, so that we have:

Area large square - Area small square  = 64 (square inches)

=> $(x+2)^{2} -x^{2} =64$

=>  $x^{2}+4x+4 -x^{2} =64$

=> 4x + 4 = 64

=> 4x = 64 - 4 = 60

=> x = 60/4 = 15 (inches)

So the length of an edge of the smaller square is 15 inches